The beam propagation method: an analysis of its applicability

Simple quantitative conditions for the applicability of the beam propagation method (BPM) in isotropic and anisotropic media are given. These conditions are derived using the operator formalism employed in the BPM in its conventional formulation. The basic limitations of the BPM are highlighted at the same time.     

Finite element beam propagation method for analysis of plasmonic waveguide

The basic idea of the finite element beam propagation method (FE-BPM) is described. It is applied to calculate the fundamental mode of a channel plasmonic polariton (CPP) waveguide to confirm its validity. Both the field distribution and the effective index of the fundamental mode are given by the method. The convergence speed shows the advantage and stability of this method. Then a plasmonic waveguide with a dielectric strip deposited on a metal substrate is investigated, and the group velocity is negative for the fundamental mode of this kind of waveguide. The numerical result shows that the power flow direction is reverse to that of phase velocity.     

On beam propagation in anisotropic media: one-dimensional analysis

We theoretically investigate light beam propagation in (1+1)D homogeneous anisotropic uniaxials where ordinary and extraordinary waves are decoupled, accounting for the vectorial character of the electromagnetic field and addressing the nonparaxial limit.     

The elliptical Laguerre–Gaussian beam and its propagation

A new kind of light beam called the elliptical Laguerre–Gaussian beam (ELGB) is proposed in this paper in terms of tensor method. The propagation formula of ELGB through axially asymmetric optical system is derived by the generalized Collins integral. By using this formula, the propagation of ELGB in free space is calculated and discussed. The results show that the propagation behavior of ELGBs is notably different from that of LGBs.     

Hollow Gaussian Schell-model beam and its propagation

In this paper, we present a new model, hollow Gaussian Schell-model beams (HGSMBs), to describe the practical dark hollow beams. An analytical propagation formula for HGSMBs passing through a paraxial first-order optical system is derived based on the theory of coherence. Based on the derived formula, an application example showing the influence of spatial coherence on the propagation of beams is illustrated. It is found that the beam propagating properties of HGSMBs will be greatly affected by their spatial coherence. Our model provides a very convenient way for analyzing the propagation properties of partially coherent dark hollow beams.     

可调谐艾里光束及其传输特性

艾里光束是一种新型无衍射光束,解决了激光在传播过程中的衍射效应。基于艾里变换技术,介绍一种可以通过椭圆平顶高斯光束产生的新型艾里光束,即可调谐艾里光束。通过理论计算,可以看出调节椭圆平顶高斯光束的束宽比可获得单尾艾里光束,同时,可调谐艾里光束的尾长可以通过调节入射椭圆平顶高斯光束的阶数来控制。通过研究,当束宽比p=1时,艾里光束的加速方向沿x轴45方向;p=1/2时,加速方向沿x轴31方向,p=1/3时,加速方向为沿x正方向,可见调节束宽比p的大小可以改变艾里光束的加速方向。     

Sine hollow beam and its propagation property

The normal sine hollow beam (NSHB) and anomalous sine hollow beam (ASHB) are proposed to describe the dark hollow beam (DHB). Based on the Collins formula, an analytical formula for NSHB (ASHB) through the ABCD optical system is derived. The intensity distributions of NSHB (ASHB) are characterized by the beam parameters and the propagation size. As the numerical example, the propagation properties of NSHB (ASHB) through the ABCD optical system have been demonstrated graphically. It is shown that NSHB (ASHB) will be evolved to the solid beam having the maximum light intensity in the beam center in free space. However, it will make the laser energy concentrate in the small area for NSHB (ASHB) through the convergent optical system.     

Application of a fully vectorial beam propagation method

A new vectorial beam propagation method has successfully been applied to a passive polarization splitter and a passive polarization converter on InGaAsP/InP. The propagating fields are calculated and the power attenuation is evaluated. The calculated crosstalk values of the splitter are in good agreement with the realized best performance. A complete polarization conversion in the converter has also been simulated. This revised version was published online in November 2006 with corrections to the Cover Date.     

Stochastic electromagnetic vortex beam and its propagation

The recent theory formulated in terms of the 2×2 cross-spectral density matrix and the propagation law of cross-spectral density are employed to investigate the stochastic electromagnetic vortex beam and its propagation characterization. Based on these, we derived the general formulae for the intensity distribution, degree of coherence and degree of polarization for stochastic electromagnetic vortex beam while propagating in free space. It is shown that the intensity distribution and the degree of polarization of the stochastic electromagnetic vortex beam propagating in free space depend on the correlation length and the topological charge of the vortex beam.     

Direct computation of higher-order propagation modes using the imaginary-distance beam propagation method

In this paper we present an extension to the standard method of eigenmode-extraction using the imaginary-distance beam propagation method. We show that it is possible to directly extract higher-order propagation modes of arbitrary shaped waveguide structures by propagating the field along the imaginary axis when the parameters are chosen in an appropriate manner. This method requires an assumption of the propagation constant of the eigenmode. In many cases this value can be determined using fast approximate techniques like the effective index method. Additionally, the approximate mode shape may be introduced as a starting condition and can further accelerate the extraction of the eigenmode. The overall number of propagation steps needed to extract multiple eigenmodes is then significantly smaller than in the case when extracting the modes sequentially with the former method.     

The threaded BPM: A novel extension to the two-dimensional scalar beam propagation method

The two-dimensional scalar beam propagation method (BPM) is a widely used, computationally efficient tool for the analysis of planar optical waveguides and devices. The inherent paraxial limitations and rectilinear analysis grid limit its application to slightly curved structures and waveguides. In this novel extention to the BPM algorithm, the curvature restrictions are removed and in many cases the paraxial restrictions can be avoided, allowing for the first time, the efficient analysis of arbitrarily curved structures, such as S- or U-shaped bends, curved transitions of progressively varying curvature, and curved couplers. It can also handle concatenated devices and the curved interconnect sections between them. The process operates by the concatenation of micro-conformal maps, which progressively re-orientate the problem optimally towards a straight BPM analysis.     

Improving the beam propagation method for TM polarization

The beam propagation method (BPM) has been widely used in numerical simulations of optical waveguides that vary slowly in the propagation direction. However, when BPM is used over a large propagation distance, a significant amplitude error in the coefficient of the leading propagating mode can be observed. Energy-conserving corrections and the single scatter approximation have been used to improve the accuracy of the BPM.     

光线庞加莱球法构建的结构光场及其传输特性研究

结构光场在光信息传输、显微成像以及微粒俘获中有重要作用.本文基于光线庞加莱球法结合不同花瓣数的梅花曲线构建了一类结构光束.根据光线庞加莱球法可计算这类光束在束腰面上的光强与相位分布,以及光束内外焦散线的分布.这些焦散线的特征表明梅花形结构光束具有无衍射与自修复的特性.进一步采用角谱衍射法和光线追迹研究了这类光束在空间中的传输特性.当梅花花瓣数为0时,该光束退化为拉盖尔-高斯光束;当花瓣数为1时,内焦散线汇集到两点,使光束具有无衍射特性.通过光线庞加莱球法获得其光线在空间传播的轨迹,直观地展示了光束被遮挡后的自修复特性.此外,本文还展示了花瓣数为5的结构光束,其内焦散线为十角星结构,该光束同样具有自修复特性.通过修改梅花曲线参数或选择其他庞加莱球面曲线可以构造更加复杂的结构光场.     

Hypergeometric Gaussian beam and its propagation in turbulence

We study propagation characteristics of hypergeometric Gaussian beam in turbulence. In this context, we formulate the receiver plane intensity using extended Huygens–Fresnel integral. From the graphical results, it is seen that, after propagation, hypergeometric Gaussian will in general assume the shape of a dark hollow beam at topological charges other than zero. Increasing values of topological charge will make the beam broader with steeper walls. On the other hand, higher values of hollowness parameter will contract into a narrower shape. Raising the topological charge or the hollowness parameter individually will cause outer rings to appear. Both increased levels of turbulence and longer propagation distances will accelerate the beam evolution and help reach the final Gaussian shape sooner. At lower wavelengths, there will be less beam spreading.     

非均匀拉盖尔-高斯关联光束及其传输特性

提出了一种新型特殊关联部分相干光束即非均匀拉盖尔-高斯关联光束,其在x和y方向上的关联结构函数分别为非均匀关联和拉盖尔-高斯关联函数.基于广义惠更斯-菲涅耳衍射积分公式,推导了这种光束交叉谱密度函数在自由空间以及大气湍流中的传输式,并计算了该光束经过自由空间和湍流大气传输的光强分布和关联结构函数分布演化特性.研究发现,该光束光强分布在传输过程中展现出自聚焦、自偏移和自分裂等奇异特性,同时发现控制关联结构函数参数可以有效地降低湍流大气的影响.关联结构调控为操控光束传输行为提供了一种新颖而有效的手段,在大气激光通信、微粒操控等领域具有重要的应用前景.     

Modified hollow Gaussian beam and its paraxial propagation

A model named modified hollow Gaussian beam (HGB) is proposed to describe a dark hollow beam with adjustable beam spot size, central dark size and darkness factor. In this modified model, both the beam spot size and the central dark size will be convergent to finite constants as the beam order approaches infinity, which are much different from that of the previous unmodified model, where the beam spot size and the central dark size will not be convergent as the beam order approaches infinity. The dependences of the propagation factor of modified and unmodified HGBs on the beam order are found to be the same. Based on the Collins integral, analytical formulas for the modified HGB propagating through aligned and misaligned optical system are derived. Some numerical examples are given.     

Bidirectional beam propagation method based on the method of lines for the analysis of photonic band gap structures

The bidirectional beam propagation method based on the method of lines is proposed as an innovative and efficient algorithm to investigate the optical properties of photonic band gap (PBG) structures. A few examples illustrate the application of this technique to the modeling of passive, lossy and active one-dimensional and index confined PBG structures. The algorithm results are validated by comparison with those obtained via the transfer matrix method, the mode-matching method and the finite difference time domain method. With respect to these methods, the present algorithm exhibits accurate results with reduced computer resources.     

Application of the beam propagation method to diffused transmission gratings

In this paper results for the diffraction characteristics of phase gratings calculated by the beam propagation method and by a rigorous integral equation method are presented, with the latter results serving as a reference. The configurations under consideration have refractive index changes which are realistic for ion exchange processes in glass. Thus, multiple reflections have only little influence which makes the beam propagation method applicable to the problem. Typically, the diffraction efficiencies computed by both methods differ by less than 2%. In contrast to the integral equation method, the beam propagation method works with a definable lateral field profile, enabling the modelling of a grating within a complete device design including the near field pattern. This revised version was published online in November 2006 with corrections to the Cover Date.     

离轴径向偏振光束及其传输特性

基于Wolf近轴传输理论, 导出离轴径向偏振光束光强的解析表达式, 并研究离轴量对离轴径向偏振光束传输中光强分布的影响, 同时根据一阶矩质心位置的定义推导出离轴径向偏振光束的质心坐标, 研究其质心位置的变化规律. 结果表明, 与径向偏振光束不同, 离轴径向偏振光束在近场处传输时光强分布不均匀, 随着传输距离的增加, 光强分布均匀性逐渐得到改善, 而径向偏振光束在传输中始终保持空心对称光斑. 离轴量较小时, 近场处光强分布呈非对称空心面包圈形, 随着传输距离增达到一定程度, 光强分布演化为对称空心面包圈形, 离轴量越小, 演变距离越短; 离轴量较大时, 随着光束的传输离轴径向偏振光束的空心部分消失, 逐渐由空心面包圈形向高斯型演变, 径向偏振光束特性消失. 另一方面, 离轴径向偏振光束的质心不随传输距离的改变而改变. 质心纵坐标恒为零, 质心横坐标与光斑尺寸及离轴量相关. 随着光斑尺寸增大, 质心横坐标成线性增长. 当离轴量较小时, 质心横坐标随离轴量的增大呈非线性增长, 增长量不明显; 离轴量较大时, 质心横坐标随离轴量的增大呈线性增长, 且变化明显.     

Computation of higher-order waveguide modes by imaginary-distance beam propagation method

Abstact Yevick and Hermansson presented an efficient numerical method for calculating fundamental modes of optical waveguides. We extend their technique to higher-order eigenmodes. Using a finite-difference beam propagation method, we obtain propagation constants and field profiles for the three lowest-order TE modes in an asymmetric rib waveguide.